After the analysis of the FOPT, one can get the phase transition temperature, the phase transition strength, and the phase transition duration that are crucial for the calculation of GWs from the FOPT.
The gravitational waves from the FOPT come from bubble collision, sound waves, and the MHD turbulence [1]}. In which, generally, the sound waves constitutes the leading source of GWs,
whose energy density is
\(\Omega h^2_{\rm sw}(f)&=&2.65 \times 10^{-6}(H_*\tau _{sw})\left(\frac{\beta }{H}\right)^{-1} v_b\left(\frac{\kappa _\nu \alpha }{1+\alpha }\right)^2\nonumber \\&\times &\left(\frac{g_*}{100}\right)^{-\frac{1}{3}}\left(\frac{f}{f_{\rm sw}}\right)^3 \left(\frac{7}{4+3 \left(f/f_{\rm sw}\right)^2}\right)^{7/2},\) 
